Is the relationship between y and x linear?
x y
0 2
4 5
8 8
12 11
i don't think it's linear.
Why not?
because i can't write an equation for y.
If you assume that Y is linear, then you can write down an equation. Then you take the first two points to completely fix the undetermined constants in that equation.
Then you have arrived at the following conclusion:
Assuming that the relation is linear, y is given in terms of x as follows...
Then you check if the other points are consistent with this equation. If the relation is linear, they must be consistent with that equation. So, if it is not, then the relation cannot be linear.
I don't think y is linear. If it is, what's the equation? y=.....
To determine if the relationship between y and x is linear, we can plot the given data points on a scatter plot. If the points form a straight line, the relationship is linear. If the points do not form a straight line, the relationship is not linear.
Let's plot the given data points (x, y) = (0, 2), (4, 5), (8, 8), and (12, 11) on a graph:
x-axis: 0, 4, 8, 12
y-axis: 2, 5, 8, 11
The scatter plot of the points does not form a straight line. Instead, it appears to have a slight curve. Therefore, we can conclude that the relationship between y and x is not linear.